Consider the following information: Your portfolio is invested 30 percent each i

Question

Consider the following information: Your portfolio is invested 30 percent each in A and C and 40 percent in B. What is the expected return of the portfolio? (Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).) What is the variance of this portfolio? (Do not round intermediate calculations. Round your answer to 5 decimal places(e.g., 32.16161).) What is the standard deviation of this portfolio? (Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).)

Explanation / Answer

1. Expected return of a Portfolio:

to find the expected return of a portfolio first we need to find expected return for the individual stock's.

Now, we will calculate expected return of portfolio = sum of weights * expected retun of stocks

= 30% *0.1171 + 40%*0.1184 + 30% * 0.10894

=0.03531 + 0.04736 + 0.032682

=0.115352

=11.53% is the expected return of the portfolio.

2. Variance of the portfolio:

the variance of the portfolio is 2 (rp) = w 2 a 2 (ra) + w 2 b 2 (rb) + w 2 c 2 (rc ) + 2wawb cov(ra,rb) + 2wawc cov(ra,rc ) + 2wbwc cov(rb,rc ),

here, we know w= weights i.e, for a and c its 30% and for b = 40%

now we will calculate 2 = standard deviation for each stocks

let us find Covariance for the stocks :cor(X,Y)=cov(X,Y) / sd(X)sd(Y)

therefore, variance of the portfolio is 2 (rp) = w 2 a 2 (ra) + w 2 b 2 (rb) + w 2 c 2 (rc ) + 2wawb cov(ra,rb) + 2wawc cov(ra,rc ) + 2wbwc cov(rb,rc ),

=(.3)2 * (0.12)2 +(.4)2 * (0.037)2 +(.3)2 * (0.198)2 +2 * 0.3 * 0.4 *-0.0012 + 2 * 0.3 * 0.4 *-0.01 + 2 * 0.3 * 0.3 *0.013

=0.09*0.0144+ 0.16*0.0014+ 0.09*0.039 - 0.00029 - 0.0024 + 0.00234

=0.00129 + 0.00022+ 0.0035- 0.00029 - 0.0024 + 0.00234

=0.00467 is the variance of the portfolio

3. standard deviation of the portfolio = squareroot of varinace

= squareroot of 0.00467 = 0.0683 is the standard deviation of portfolio.

=6.83% is the standard deviation

state of economy probability stock A stock B stock C expected return of A = stock * probability expected return of B= stock * probability expected return of C= stock * probability Boom 0.19 .360 .460 .340 0.0684 0.0874 0.0646 Good 0.41 .130 .110 .180 0.0533 0.0451 0.0738 Poor 0.31 .020 .030 -.066 0.0062 0.0093 -0.02046 Burst 0.09 -.120 -.260 -.100 -0.0108 -0.0234 -0.009 Expected return of each stock = sum of all 0.1171 0.1184 0.10894

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